Correlation test

# Correlation test

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# How would you define a correlation test?

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# Correlation tests association💕

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# Correlation evaluates the __linear__ association between two or more variables.
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# How many methods to perform correlation analysis you know?
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## Different methods to perform correlation analysis depending on data type

<img src="img/pearson-correlation-spearman-correlation-linear-regression-6-638.png" width="50%" style="display: block; margin: auto;" />
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## Most widely used method is Pearson's

<img src="img/pearson_blue.png" width="60%" style="display: block; margin: auto;" />
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## Example: comparing the correalation between two replicates of a gene expresion experiment

These are two continues values and **might** followed a normal distribution.

We need to check that the later is true.

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# Pearson correlation

Pearson correlation (r) measures the linear dependence between two variables.

r comes linear regression curve uppon plotting of y = f(x).

To calculate r:
<img src="img/correlation_coefficient_formula.jpg" width="40%" style="display: block; margin: auto;" />
And to calculate the significance associated to it. 
<img src="img/correlation_coefficient_formula_t.png" width="15%" style="display: block; margin: auto;" />

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# Other correlation methods

Ranking: Spearman & Kendall

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# Showing association

To show association, variables are plotted as scatterplot

<img src="img/scatter.png" width="40%" style="display: block; margin: auto;" />
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# R functions for correlation

- Base R
    - cor(iris$Sepal.Length, iris$Petal.Length, method = c("pearson"),na.rm = TRUE)
    - cor(iris$Sepal.Length, iris$Petal.Length, method = c("spearman"))
  + cor.test(iris$Sepal.Length, iris$Petal.Length,method=c("pearson"))
- library(corrplot)
    corrplot(cor(iris[,1:4]))
- library(Hmisc)
   rcorr(as.matrix(iris[,1:4]))
    
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# Let's dive in some proteomics data and explore correlation across replicates!
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